(a) The cross-section for scattering of muons with air at atmospheric pressureis 0.1 barns, and the natural lifetime of muons 2.2 x 10-6 s. Explain whatis meant by the terms elastic scattering and lifetime. Which of these fac-tors limits the distance over which a beam of muons can travel in air in alaboratory, if the muon velocity is 106 ms-¹?(Assume number density of air at STP = 2.69 × 1025 m−³)(b) Given your answer to (a), why is it possible to detect showers of muons atground level caused by the impact of primary cosmic ray particles with airat around 12 km altitude? Given that the mean energy of muons detectedat ground level is 4 GeV, calculate the distance (in air) over which thenumber of such muons in a beam would reduce by a factor of e. What kindof interactions contribute to the scattering cross-section for these particles?[1 barn = 10-28 m²; mass of muon = 105 MeV/c²; number density of airat STP = 2.69 x 1025 m-³]

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(a) The cross-section for scattering of muons with air at atmospheric pressu is 0.1 barns, and the natural lifetime of muons 2.2 × 10−6 s. Explain wh is meant by the terms elastic scattering and lifetime. Which of these fa tors limits the distance over which a beam of muons can travel in air in laboratory, if the muon velocity is 106 ms-¹? (Assume number density of air at STP = 2.69 × 10²5 m-³) (b) Given your answer to (a), why is it possible to detect showers of muons ground level caused by the impact of primary cosmic ray particles with a at around 12 km altitude? Given that the mean energy of muons detecte at ground level is ~ 4 GeV, calculate the distance (in air) over which t number of such muons in a beam would reduce by a factor of e. What kin

(a) The cross-section for scattering of muons with air at atmospheric pressu is 0.1 barns, and the natural lifetime of muons 2.2 × 10−6 s. Explain wh is meant by the terms elastic scattering and lifetime. Which of these fa tors limits the distance over which a beam of muons can travel in air in laboratory, if the muon velocity is 106 ms-¹? (Assume number density of air at STP = 2.69 × 10²5 m-³) (b) Given your answer to (a), why is it possible to detect showers of muons ground level caused by the impact of primary cosmic ray particles with a at around 12 km altitude? Given that the mean energy of muons detecte at ground level is ~ 4 GeV, calculate the distance (in air) over which t number of such muons in a beam would reduce by a factor of e. What kin